We are trying to aggregate the preferences of three different individuals (Anna, Brian, and Chris) over three alternatives (movies, sports, and clubbing) in a democratic way. As shown below, Anna prefers movies to sports and sports to clubs, and thus movies to clubs; Brian prefers sports to clubs and clubs to movies, and thus sports to movies; finally, Chris prefers clubs to movies and movies to sports and, therefore, clubs to sports. We can construct indifference curves maps (utility functions) for the three of them because, for each of them as individuals, their preferences are well behaved (transitive; i.e., if A is preferred to B and B is preferred to C, then A is preferred to C).

Anna movies sports clubs

Brian sports clubs movies

Chris clubs movies sports

When we aggregate, we say that A is preferred to B if the majority prefers A to B. Answer the following questions, explaining your answer:

(a) Are movies preferred to sports or sports to movies?

(b) Are sports preferred to clubs or are clubs preferred to sports?

(c) Are movies preferred to clubs or are clubs preferred to movies?

(d) Are the aggregate preferences transitive?

(e) Can we construct an aggregate utility function (aggregate indi⁄erence curves map)?